共查询到19条相似文献,搜索用时 47 毫秒
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孤子族的生成及换位表示的一般结构 总被引:2,自引:0,他引:2
本文通过对谱问题ψx=U(u,λ)ψ的直接研究,利用谱梯度提供一条获得孤子方程族的途径,进一步,我们给出了孤子方程换位表示的一般结构,同时我们还将看到同一个谱问题可产生两族不同的孤子发展方程。 相似文献
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The involutive solutions of soliton hierarchy are given in this paper.Through the nonlinearization of the lax system for solition hierarchy,it is proven that the involutive solution of compatible systems(H)(spatial part)and(Fm)(time part)is mapped into the soliton of solutin hirarohyby the mapping f which is determined by the constraint relation u=f(ψ)between potentials and eigenfunotions. 相似文献
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在Hirota方法中,判定Hirota条件是一个重要课题,至今尚未完全解决.一般,出现在Hirota条件中的函数Ω(p)为多项式或根式.本文通过讨论Boussinesq型方程的孤子解,提供了在Ω(p)为根式情形下否定Hirota条件的一个途径. 相似文献
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李壹宏 《纯粹数学与应用数学》2013,(3):287-292
利用检验函数定义弱解的方法来求解含有任意常数k1,k2的目标方程的单孤子解.给出了目标方程的单孤子解与任意常数k1,k2的关系. 相似文献
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刘萍 《数学物理学报(A辑)》2009,29(5):1213-1222
根据广义耦合KdV孤子方程的Lax对, 借助谱问题的规范变换, 一个包含多参数的达布变换被构造出来. 利用达布变换来产生广义耦合KdV孤子方程的偶孤子解, 并且用行列式的形式来表达广义耦合KdV孤子方程的偶孤子解. 作为应用, 广义耦合KdV孤子方程的偶孤子解的前两个例子被给出. 相似文献
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借助谱问题的规范变换, 给出广义耦合KdV孤子方程的达布变换,利用达布变换来产生广义耦合KdV孤子方程的奇孤子解,并且用行列式的形式来表达广义耦合KdV孤子方程的奇孤子解.作为应用,广义耦合KdV孤子方程奇孤子解的前两个例子被给出. 相似文献
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高维代数簇的半线收缩已具有很多研究。将它们推广到极面收缩对高维簇的双有理分类理论是很有意义的。设X是非奇异的n维射影簇,L是X上的ample除子,f:X→Y是以Kx(n-3)L为支撑除子的极面收缩映射。当f不是双有理映射,Belktrametti等人系统的研究了f的结构。本文主要研究f是双有理映射时的情形。一个完整的结构定理被给出。 相似文献
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《中国科学 数学(英文版)》2012,(6):1221-1228
In this paper,we derive an estimate on the potential functions of complete noncompact gradient shrinking solitons of Ricci-harmonic flow,and show that complete noncompact gradient shrinking Ricci-harmonic solitons have Euclidean volume growth at most. 相似文献
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YUAN Hongjun 《数学年刊A辑(中文版)》2001,(3):361-380
The aim of this paper is to discuss
the instantaneous shrinking and localization of the support
of functions in $\hbox{Y}_{\lambda}(m,p,q,N)$ and their
applications to some nonlinear parabolic equations including
the porous medium equation
$
u_t=\Delta u^m-u^{q},\ m>0,\ q>0
$
and the $p$-Laplace equation
$
u_t=\hbox{div}(|\nabla u|^{p-2}\nabla u)-u^{q},\ p>1,\ q>0.
$
In particular, as an application of the results,
the necessary and sufficient condition for the solutions
of the above $p$-Laplace equation with
nonnegative finite Borel measures
as initial conditions to have the instantaneous shrinking property
of the support is obtained. This is an answer to an open problem
posed by R.~Kersner and A.~Shishkov. 相似文献
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YUAN Hongjun 《数学年刊B辑(英文版)》2001,22(3):361-380
61. IntroductionAs well knoWn, the solutionS of semilinear Parabolic equations at = An -- ac, 0 < q < 1have the ISS (the thetantaneous shrinking of the support) ~erty (see 11--5]).Such PrOPerty is d~d as follows.Defiallion 1.1. A hoction u E La(Q) is sold to haw the ISS p~rty, ijjor augr > 0, there hots a POsiboe n~ber R = R(T) such thatu(z, t) = 0for a. e. (z,t) e (R" \ Ba) x (T, co), tDhere AN is the N-dimensional Euclidean space,and Q = AN X (0, co).UP to the preseDt, there… 相似文献
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Hong Xin Guo 《数学学报(英文版)》2010,26(7):1299-1308
In this paper, we derive evolution equation of the integral of the Gauss curvature on an evolving hypersurface. As an application, we obtain a monotone quantity on the level surface of the potential function on a 3-dimensional steady gradient Ricci soliton with positive sectional curvature, and prove that such a soliton is rotationally symmetric outside of a compact set under a curvature decaying assumption. Along the way we will also apply our evolution equation to some other cases. 相似文献
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本文研究了完备非紧且Ricci曲率正有界的n维K(a)hler流形上的单值化问题,利用Sobolev不等式,L2估计和Bézout估计和Gauss-Bonnet积分方法,得到了一个单值化定理,推广了流形为有限拓扑型的结果. 相似文献
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段孝娟 《数学物理学报(B辑英文版)》2018,38(1):269-288
In this paper, we explicitly construct some rotationally symmetric gradient pseudoK¨ahler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss the "phase change" phenomenon caused by the variation of parameters. 相似文献